Hausdorff dimension method reduces the error of box counting
Zhenyu Jin · Theoretical and Natural Science · 2023
The Hausdorff dimension of an object is a topological measure of the size of its covering properties. To compute the Hausdorff dimension of an object, this report reviews the method of box counting, a method of gathering data for analyzing complex patterns by breaking a dataset, object, image, etc. into smaller and smaller pieces, typically "box"-shaped, and analyzing the pieces at each smaller scale. However, in this process, errors are always generated because of the extreme cases in which boxes are just covered with a small corner of the pattern but still should be counted. As a result, the number of boxes counted becomes larger than usual resulting in inaccurate results. In order to reduce the error in the final result, this report applies an improvement to this method to reduce the errors in the result and provides the example of Koch snowflake, and also examines the effect of the improvement.